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MATH

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Posts

  • ThatDudeOverThereThatDudeOverThere MY FINEST CREATION oh nevermind it's deadRegistered User regular
    edited May 2008
    Straightzi wrote: »
    Larlar wrote: »
    Framling wrote: »
    Larlar wrote: »
    Fram, you should talk to nap. He's in his own private math universe.

    I was in there once. We picked up a couple of eigenvalues and went to see The Matrix.

    I remember once the conversation had turned to big numbers and he threw out something and I just came right back with either g_64 or A(g_64,g_64), I can't remember which, but he was just like "Damn, you don't fuck around, do you?"

    (I do not.)

    But yeah, I get the feeling we're in about the same boat, finding really it fascinating but not being very good at actually working through it all.

    Sometimes I think Graham brought attention to that number just to spite the future. Seems to be the growing trend. Another 500 years from now, math and sadism will be considered the same fetish.

    At what point in the future does math become a fetish?
    g_64 years from now

    nHu0VJL.png
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  • JedocJedoc Registered User regular
    edited May 2008
    I hate trying to conceptualize big numbers. Just freaks me the hell out. Like a googol.
    Exit Mundi wrote:
    One ‘googol’ years, is the official word for that number. It’s the current age of the Universe, one billion billion billion billion billion billion billion billion billion billion times over. Squeeze the entire history of our Universe into the thickness of a dollar bill, and one googol years would give you a pile of money that reaches one hundred quadrillion quadrillion quadrillion quadrillion light years high. It wouldn’t even fit in our Universe.

    Fuck that noise.

    I don't want to even try to think about g_64, just in case I accidentally manage to. Somebody finds me in my apartment days later. Brains, hair, and tiny little digits plastered to all the walls and ceiling.

    cannon.jpg
  • cruciverbietecruciverbiete Registered User
    edited May 2008
    il faut calculer pour vivre et non vivre pour calculer

    also, my old phone number almost fits perfectly at a certain point in pi

  • autono-wally, erotibot300autono-wally, erotibot300 love machine Registered User regular
    edited May 2008
    What's the problem with big numbers. They're just big. Who cares how often something would fit into the universe were it made of something you can imagine?
    Personally I'm not a fan of ONE specific mathematical discipline, but I like sequences and series

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  • redheadredhead Registered User
    edited May 2008
    il faut calculer pour vivre et non vivre pour calculer

    also, my old phone number almost fits perfectly at a certain point in pi

    I'm pretty sure all phone numbers fit perfectly at some point in pi

  • cruciverbietecruciverbiete Registered User
    edited May 2008
    redhead wrote: »
    Spoiler:

    I'm pretty sure all phone numbers fit perfectly at some point in pi

    in sequence?
    6 numbers in a row is pretty cool
    especially since they're pretty close to the decimal mark

    i just finished my second engineering math.
    fuck cycloids

  • redheadredhead Registered User
    edited May 2008
    redhead wrote: »
    Spoiler:

    I'm pretty sure all phone numbers fit perfectly at some point in pi

    in sequence?
    6 numbers in a row is pretty cool
    especially since they're pretty close to the decimal mark

    i just finished my second engineering math.
    fuck cycloids

    well, close to the decimal is a different matter

    but I mean you've got an infinite number of digits to work with back there if you count far enough, so every 6 digit sequence kind of has to appear somewhere

  • autono-wally, erotibot300autono-wally, erotibot300 love machine Registered User regular
    edited May 2008
    our math professor is the worst. he just reads his lectures he wrote thirty years ago on a typewriter and always does the same exams, only with slightly different numbers.
    It's a joke really, and hadn't I taken some other math courses before I wouldn't learn a thing
    But this way when a problem comes up, I just take one of my trusty books and learn it myself

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  • cruciverbietecruciverbiete Registered User
    edited May 2008
    we could replace every phonebook in the world with one book
    Spoiler:

  • autono-wally, erotibot300autono-wally, erotibot300 love machine Registered User regular
    edited May 2008
    Is there a way to get truely random numbers, without measuring random events? I was always wondering this.

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  • cruciverbietecruciverbiete Registered User
    edited May 2008
    i remember reading about random phenomenae
    from what i remember (Science, 2004ish so probably outdated), it's hardly random.
    a few are statistically close, such as movement of alpha particles, i think.

  • KingAgamemnonKingAgamemnon Registered User
    edited May 2008
    Things like linear algebra and calculus and geometry are means to an end. They are called elementary maths because they form the basic foundation for understanding and applying even more interesting and complicated things.

    Set theory is where I'm resting my head at the moment. All math is encompassed by set theory. Ofcourse, I've only got experience with undergrad math.

  • FramlingFramling Registered User regular
    edited May 2008
    Jedoc wrote: »
    I hate trying to conceptualize big numbers. Just freaks me the hell out. Like a googol.
    Exit Mundi wrote:
    One ‘googol’ years, is the official word for that number. It’s the current age of the Universe, one billion billion billion billion billion billion billion billion billion billion times over. Squeeze the entire history of our Universe into the thickness of a dollar bill, and one googol years would give you a pile of money that reaches one hundred quadrillion quadrillion quadrillion quadrillion light years high. It wouldn’t even fit in our Universe.

    Fuck that noise.

    I don't want to even try to think about g_64, just in case I accidentally manage to. Somebody finds me in my apartment days later. Brains, hair, and tiny little digits plastered to all the walls and ceiling.

    Don't worry, you can't. It's hopelessly huge. a googol you can actually write out. You can fit that shit on a piece of paper. g_64, no way. You can't even write out the number of digits in it. You can't write out the number of digits in the number of digits in g_64. You can't even write down the number of levels of digit-counting you would have to go through to get to something you could write down.

    If you were to turn the entire universe into a computer capable of representing a digit with each individual particle, and were to crank the speed up so that you were refreshing every Planck time (the theoretical smallest possible interval at which time can be distinguished from space, something like 5*10^-44 seconds), over the entire lifetime of the universe, you wouldn't even have covered a perceptible fraction of g_64.

    Here's the mind-fuck, though:
    Spoiler:

    you're = you are
    your = belonging to you

    their = belonging to them
    there = not here
    they're = they are
  • StraightziStraightzi The rock, the vulture, and the chain All that the proud can feel of painRegistered User regular
    edited May 2008
    Jesus Christ Fram I hate you.

  • TossrockTossrock too weird to live too rare to dieRegistered User regular
    edited May 2008
    redhead wrote: »
    il faut calculer pour vivre et non vivre pour calculer

    also, my old phone number almost fits perfectly at a certain point in pi

    I'm pretty sure all phone numbers fit perfectly at some point in pi

    Well, it goes further than that

    everything is somewhere in pi

    Think about it: Because it never repeats, and continues infinitely, it must at some point take every possible combination of numbers

    which means everything, everything is represented somewhere in it's digits. Hamlet in standard ASCII. The numbers one through four in such a sequence so that, if mapped to the letters TAGC, they would represent your genetic code. A jpeg of your face. A binary video file of your entire life, from birth to death.

    Now that's a mindfuck.

  • TossrockTossrock too weird to live too rare to dieRegistered User regular
    edited May 2008
    Tossrock wrote:
    represented somewhere in it's digits

    INAPPROPRIATE APOSTROPHE

    I hate being jailed :/

  • quibblebarfquibblebarf Registered User regular
    edited May 2008
    Kovak wrote: »
    musanman wrote: »
    Kovak wrote: »
    Also, musaman, arbitrarily saying things like "you must argue this point using no mathematics, in order to be interesting" is ridiculous. I'll argue things how they need to be argued.

    honestly coming in and demanding that mathematical facts be proven without math is a bit like

    going to church and asking the preacher to explain everything without god

    or even speaking

    he's just gotta wave his dick around

    ok I'll show my hand...

    I teach algebra and statistics and both of these subjects involve this discussion. You can't argue with 9th graders using mathematics like a gamma function. I am not satisfied saying "because"

    I would like to keep the conversation going, so more points of view are better.

    Honestly, even the definition of the simple factorial function is defined from 1 to infinity and just sets 0! as 1.

    My lining up way works as one of the simplest reasons to explain why it's gotta be 1 is in probability calculations.

    There really is no "simple" and sound mathematical proof.

    Your students need to learn that sometimes they just gotta accept something till they get smarter

    I'd argue it on the aesthetics. With 0! = 1 you get a nice, simple primitive recursive function, namely

    f(0) = 1
    f(n+1) = f(n) * n

    If 0! were something other than 1, you'd define !n as f(n) everywhere except 0, where it would disagree. If your students argue about the natural numbers starting at 1, tell them about Peano's axioms.

  • SirToastySirToasty Registered User regular
    edited May 2008
    Framling wrote: »
    Here's the mind-fuck, though:
    Spoiler:
    Hahahaha

    I love math.
    Spoiler:

  • Simon MoonSimon Moon Registered User regular
    edited May 2008
    Tossrock wrote: »
    Think about it: Because it never repeats, and continues infinitely, it must at some point take every possible combination of numbers

    Sorry, pet peeve:

    Pi is, in fact, sufficiently random that any string of digits appears within its decimal expansion with probability one. However, never repeating is not sufficient for this amount of randomness.

    Consider: Let alpha be the sum of 10^-n! as n goes from 0 to infinity (for those who read TeX, /alpha = /Sum_{n=0}^{/infty} 10^{-n!}). It can be shown that alpha is not merely irrational, alpha is transcendental, (i.e. There's no polynomial with rational coefficients such that alpha is the root of that polynomial) however irrationality is enough for alpha to consist of an infinite string of digits that never repeats. But the only digits in the decimal expansion of alpha are 0 and 1. Thus, it cannot, e.g., contain your mom's phone number.

    Steam: simon moon
  • FramlingFramling Registered User regular
    edited May 2008
    Tossrock wrote: »
    redhead wrote: »
    il faut calculer pour vivre et non vivre pour calculer

    also, my old phone number almost fits perfectly at a certain point in pi

    I'm pretty sure all phone numbers fit perfectly at some point in pi

    Well, it goes further than that

    everything is somewhere in pi

    Think about it: Because it never repeats, and continues infinitely, it must at some point take every possible combination of numbers

    which means everything, everything is represented somewhere in it's digits. Hamlet in standard ASCII. The numbers one through four in such a sequence so that, if mapped to the letters TAGC, they would represent your genetic code. A jpeg of your face. A binary video file of your entire life, from birth to death.

    Now that's a mindfuck.

    I'd just like to point out that it's not necessarily the case that a sequence that never repeats and continues infinitely will at some point contain every possible combination.

    For instance, if you were to take the digits of pi pi and replace each 8 with a 4, you'd still have a non-repeating infinite sequence of digits, but it will never contain Jenny's phone number. Similarly, there are a lot of patterns that will never appear in 1.101001000100001000001000000100000001... even though it never repeats and continues infinitely.

    Now, this does indeed seem to be the case with pi, and its digits do conform to roughly the same distribution as would be expected by random noise in the long term, but that's not a consequence of its infinite non-repetition.

    Here's an interesting question to which I do not know the answer: is there a point in the decimal expansion of pi where it repeats everything that has gone before? I don't mean repeating in the standard sense, I mean, say it started 3.14159265358979314159265358979323846, i.e. it repeats everything that has come before and then continues with other, non-repeated digits. It seems like this would have to happen, but I can't say with certainty.

    I would also asume that if this could occur at all, it would occur an infinite number of times.

    you're = you are
    your = belonging to you

    their = belonging to them
    there = not here
    they're = they are
  • SmasherSmasher Starting to get dizzy Registered User regular
    edited May 2008
    I'm no math major, but I'll give this a shot:

    For a given digit index n, the probability that this digit ends a string of length n (ie, everything up to that digit) which is then repeated by the next n digits is 1/(10^n). The sum of this series as n goes to infinity is simply .1111..., or 1/9. In other words, the chance of there being any such sequence at all is 1/9; Thus I would conclude that there is almost surely not an infinite number of such sequences.

    This of course assumes the digits of pi are randomly distributed; if somehow it turns out they're not then who knows.

  • Me Too!Me Too! __BANNED USERS regular
    edited May 2008
    This is sorta related to math
    The autistic savant who sees numbers as images in his mind amazes me
    He can do these incredibly complex calculations simply by describing the picture he sees in his head
    Also the dude recited pi to an obscene number of places

  • BusterKBusterK Negativity is Boring Cynicism is Cowardice Registered User regular
    edited May 2008
    Lol! wrote: »
    This is sorta related to math
    The autistic savant who sees numbers as images in his mind amazes me
    He can do these incredibly complex calculations simply by describing the picture he sees in his head
    Also the dude recited pi to an obscene number of places

    You mean the Rain Man guy?
    Or the guy who isn't actually autistic but still has the mind like a savant?

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  • Me Too!Me Too! __BANNED USERS regular
    edited May 2008
    The second one
    The scary part about him reciting pi is, he didn't memorize it or anything
    No he just kept describing the picture in his head

  • BusterKBusterK Negativity is Boring Cynicism is Cowardice Registered User regular
    edited May 2008
    Lol! wrote: »
    The second one
    The scary part about him reciting pi is, he didn't memorize it or anything
    No he just kept describing the picture in his head

    The mind is a strange thing
    It was previously thought inordinate strength in one area of the brain necessarily meant retardation in another
    But that guy proved that wrong

    Visit http://www.cruzflores.com for all your Cruz Flores needs. Also listen to the podcast I do with Penguin Incarnate http://wgsgshow.podomatic.com
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  • LarlarLarlar Super Moderator, Moderator, ClubPA mod
    edited May 2008
    Smasher wrote: »
    I'm no math major, but I'll give this a shot:

    For a given digit index n, the probability that this digit ends a string of length n (ie, everything up to that digit) which is then repeated by the next n digits is 1/(10^n). The sum of this series as n goes to infinity is simply .1111..., or 1/9. In other words, the chance of there being any such sequence at all is 1/9; Thus I would conclude that there is almost surely not an infinite number of such sequences.

    This of course assumes the digits of pi are randomly distributed; if somehow it turns out they're not then who knows.

    It's been so long since I've done anything math-related that I'll pretty much agree with anything that remotely makes sense, but that seems right (at least for the first occurrence, because once it happens and takes up a span of 2n digits, it's impossible for it to happen again until at least 4n; and even though pi is infinite I'm sure that still slightly affects the probability of it reoccuring...god, I hate statistics).

    But if pi truly is random and infinite and, for any sequence of infinitely large ns the probability of this occurring doesn't ever reach/approach 0 (and this is what I'm trying to think about now), then Fram's probably right and it would be expected to occur an infinite number of times, however infinitely spaced out the n-point of each occurrence would be from one another.

    iwantanswers3.png
  • ThatDudeOverThereThatDudeOverThere MY FINEST CREATION oh nevermind it's deadRegistered User regular
    edited May 2008
    Framling wrote: »
    Don't worry, you can't. It's hopelessly huge. a googol you can actually write out. You can fit that shit on a piece of paper. g_64, no way. You can't even write out the number of digits in it. You can't write out the number of digits in the number of digits in g_64. You can't even write down the number of levels of digit-counting you would have to go through to get to something you could write down.

    If you were to turn the entire universe into a computer capable of representing a digit with each individual particle, and were to crank the speed up so that you were refreshing every Planck time (the theoretical smallest possible interval at which time can be distinguished from space, something like 5*10^-44 seconds), over the entire lifetime of the universe, you wouldn't even have covered a perceptible fraction of g_64.

    Here's the mind-fuck, though:
    Spoiler:

    I think my brain just exploded.

    nHu0VJL.png
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  • CorporateGoonCorporateGoon Registered User regular
    edited May 2008
    This place will let you search the first 200 million digits of pi for pretty much whatever number you want.

    The string 5318008 occurs at position 13,809,596... so, clearly the universe got bored one day and decided to screw around with its calculator.

  • OrestesOrestes Registered User
    edited May 2008
    I once read that there are varying degrees of infinity.

    Such as there is an infinite amount of numbers between 0 and 1. However, there are the exact same amount of infinite numbers between 0 and 2.

    The weird part is, if you take the amount of rational real numbers between 0 and 1 (1/2, 1/3, 1/4, 1/5, etc.), they are dwarfed by the amount of irrational real numbers between 0 and 1.

    Or something like that.

    I never really paid attention, I just seemed to recall the jist of it

  • JunpeiJunpei Registered User regular
    edited May 2008
    That goes back to the A_0, A_1 post that Framling made earlier. Check back a couple of pages, then once you've done that read up about g_64.

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  • L|amaL|ama Registered User regular
    edited May 2008
    Lol! wrote: »
    This is sorta related to math
    The autistic savant who sees numbers as images in his mind amazes me
    He can do these incredibly complex calculations simply by describing the picture he sees in his head
    Also the dude recited pi to an obscene number of places

    Was that the guy who learned icelandic in like a week? That shit is just ridiculous.

  • LarlarLarlar Super Moderator, Moderator, ClubPA mod
    edited May 2008
    Orestes wrote: »
    The weird part is, if you take the amount of rational real numbers between 0 and 1 (1/2, 1/3, 1/4, 1/5, etc.), they are dwarfed by the amount of irrational real numbers between 0 and 1.

    Or something like that.

    You should look into countable vs uncountable sets. The most common example is the rational vs irrational sets. It's pretty neat...I'd explain it, but I'm not Framling. I can't remember shit.

    iwantanswers3.png
  • OrestesOrestes Registered User
    edited May 2008
    Graham's Number is not new, nor is it interesting anymore. Once you've had to study how the notation works, it gets pretty stupid.

    What I find more interesting is botched math proofs.

  • potatoepotatoe Registered User regular
    edited May 2008
    this thread has reminded me of why i'm glad i'm done with math classes

    I tried to write "but that" and my hands naturally wrote "butt hat", which is vastly superior in every way.
  • OrestesOrestes Registered User
    edited May 2008
    Stuff where people divide by zero and get 1 = 2 or similarly stupid stuff like that.

  • Airking850Airking850 Registered User regular
    edited May 2008
    Countable infinite sets are sets that can be mapped one-to-one onto the natural numbers {0, 1, 2, 3...}

    The Integers {...-3, -2, -1, 0, 1, 2, 3...} are a countable infinite set, because you can map them to the natural numbers; one such mapping can be achieved by mapping 0 to 0, positive numbers p to 2p and negative numbers n to -(2n - 1). So there are the same number of positive integers as there are positive and negative integers.

    The set of real numbers between 0 and 1 is an uncountable infinite set. The easiest proof of this is by a simple contradiction: If every real number is accounted for, then there must be a real number whose first digit after the decimal is different than the real number mapped to 0, whose second digit after the decimal is different than the real number mapped to 1, whose third digit after the decimal is different than the real number mapped to 2, and so on for every decimal after the digit (the number of digits after the decimal in any real number is a countable set). The real number we just defined is not represented by a natural number since it's different from every real number that's being represented by a natural number, therefore it is impossible to map all decimal numbers between 0 and 1 to the set of natural numbers. So there are more real numbers between 0 and 1 than there are integers.

  • ProlegomenaProlegomena Frictionless Spinning The VoidRegistered User regular
    edited May 2008
    Orestes wrote: »
    Graham's Number is not new


    surprisingly, the newest number of all is seven hundred and twenty one, which, despite its rather innocuous standing in the grand scheme of things, was only introduced a couple of weeks ago

  • FramlingFramling Registered User regular
    edited May 2008
    Orestes wrote: »
    Graham's Number is not new, nor is it interesting anymore. Once you've had to study how the notation works, it gets pretty stupid.

    What I find more interesting is botched math proofs.

    Botched math proofs are not new.

    Transfinite numbers are not new.

    Most of the shit in this thread is not new.

    Except to the people in the thread who've never heard of them.

    Which is kinda the point of the fucking thread.

    So, who wants to hear about Turing's incompleteness theorem and Busy Beaver functions?

    you're = you are
    your = belonging to you

    their = belonging to them
    there = not here
    they're = they are
  • PiptheFairPiptheFair Registered User regular
    edited May 2008
    PiptheFair wrote: »
    math is gay

    imo

    STEAM
    Spoiler:
  • LarlarLarlar Super Moderator, Moderator, ClubPA mod
    edited May 2008
    you're gay

    seems you and math just might hit it off after all

    iwantanswers3.png
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